A theme that keeps recurring in these posts is that the so-called "paper trained" musicians are "afraid" or "scared" to try playing without music. Maybe that's the crux of the problem. At some point in their training they were made to believe that they would sound bad or foolish if they went off the paper, and so they became unwilling to take the risk of playing "without a net." I dated a woman for a while who was a classically trained violinist, and loved Old Time. We played in a band and he insisted that she wanted to try to learn everything by ear. Once she learned the tune she played beautifully, but the learning process, even for the simplest fiddle tunes, was agonizing and frustrating. I can imagine why people who are well-trained musicians would balk at putting themselves through such a humbling experience.
Maybe this would be a good topic for another thread, but it's reminiscent of the typical statement one often hears from classically-trained singers, that they're reluctant to sing in a folk style because they're afraid that they will hurt their voice. As far as I know folk singers tend to have much longer careers than classical singers and have far fewer vocal problems. It seems that maybe fear of folk music is instilled in some classical players!